Probabilistic inverse analysis for predicting the distribution of multiple internal defects

A concept and a method of probabilistic inverse analysis are proposed for predicting the distribution of internal defects from their two-dimensional image on a cross-section. In this paper, circular (penny-shaped) cracks are chosen as a subject for analysis and a discussion is made on their statistical distribution. The spatial distribution of internal cracks, i.e. the number of cracks in a unit volume and the distribution of crack radius, is inversely predicted from the areal distribution of cracks observed on a cross-section, i.e. the number of cracks in a unit area and the distribution of crack length. When enough information on the areal distribution is given, for example, when a number of intercepted cracks can be observed on a cross-section for dense internal cracks, the spatial distribution of internal cracks is deterministically analyzed. Conversely, when the information is limited in the cross-sectional observation, a unique distribution of internal cracks cannot be determined. Then, a method of probabilistic inverse analysis is proposed. After the validity of the method is confirmed by numerical simulation, it is applied to actual internal cracks which initiate inside the specimens under a creep-fatigue condition. The distribution of internal cracks is successfully predicted.